It really, honestly will. Many major distributors already require it on PC, and it's in the console manufacturer's best interest to begin with. It 100% will happen, it's been in the tea leafs for awhile. You don't strike me as someone who was going to jump on the next console generation quickly anyway, so you should have a few more years of offline gameplay. But, as I've stressed in many posts, every new console is about the entire lifecycle of the console. People ask why the new consoles need ridiculous graphical output, but how long did it take for people to wonder why the Wii wasn't in HD? At the Wii's release, a non-HD console wasn't a terrible idea, because 1080p monitors weren't in even 5% of households yet. But now, at the end of its lifecycle, it's seen as a relic of the past. These new consoles will be outputting at least 2K definition, and there's a good chance that by the end of its lifecycle (2020), Americans will be starting to buy 4K displays.
My argument here is that a completely wired household is seen as an inevitability at this point. Internet capable TVs are already getting into new markets. Hell, this weekend I've been asked to go hook up an Internet ready TV for my grandmother's friends.
The only argument against a connection-needed console is an infrastructure one, where it's just not a possibility for some people. But that concern is fading away. It's not reality anymore that people don't have the ability to stay connected. And, as I've said, it's in the companies' best interests. When in the past hasn't that trumped all else? Microsoft had to sink tens, if not hundreds of millions into new security measures once the pirated ROM market for the 360 started to get really big. Developers are constantly looking for new ways to counter pirating, and most are going with needing a connection. Diablo III might be the biggest PC release this year, and you will have to be connected at all times to play the single player.
It's not happening; it's already happened.